A small firm intends to increase the capacity of a bottleneck operation by addin
ID: 2740167 • Letter: A
Question
A small firm intends to increase the capacity of a bottleneck operation by adding a new machine. Two alternatives, A and B, have been Identified, and the associated costs and revenues have been estimated. Annual fixed costs would be $39,000 for A and $30,000 for B; variable costs per unit would be $10 for A and $11 for B; and revenue per unit would be $15. Determine each alternative's break-even point in units. (Round your answer to the nearest whole amount.) At what volume of output would the two alternatives yield the same profit? (Round your answer to the nearest whole amount.) If expected annual demand is 16,000 units, which alternative would yield the higher profit?Explanation / Answer
1) Break even point in units = Fixed COst / sale price per unit - VC per unit
Break even point in units for A = 39000/15-10 = 7800 units
Break even point in units for B = 30000/15-11 = 7500 units
2) Let the Volume be Q
Q*(15-10 ) - 39000 = Q*(15-11)-30000
15Q-10Q-39000 = 15Q-11Q-30000
5Q-39000 = 4Q-30000
5Q-4Q = -30000+39000
Q = 9000 units
3) Expeced annual demand = 160000 units
Sales -Variable cost - Fixed COst = Profits
A) 16000*(15-10)-39000 = $41000
B ) 16000*(15-11)-30000 = $34000
Alternative A yields the higher profits